If you've ever done something in a big, excited, uninhibited way, you know what it means to do things wildly. Preschoolers might sit in a calm circle for a little while, but they're usually happier running around wildly.
Doing something wildly involves exaggerating it, or doing it in an unpredictable or uncivilized way, like a wild animal. Angry people shout and gesture wildly, and sports fans jump around and cheer wildly when their team wins an important game. The adverb wildly comes from wild and its Proto-Indo-European root that means "wild" or "woodlands."